A contour mode resonator takes the form of a thin slice of piezoelectric material and resonates within the plate of the slice of material. The thickness of the resonator must be sufficiently small so that inertial forces caused by any movements outside the plane of the slice have a negligible influence on the deformation energy thereof. The shape most usually adopted for the slice is rectangular, which entails the existence of four geometric parameters:
one or two cutting angles to define the direction perpendicular to the slice; PA1 one cutting angle to define the orientation of the sides of the rectangle in the plane of the slice; and PA1 the dimensions of the rectangle.
A known resonator, having good thermal properties and quasi-independence of the first order thermal coefficient from the dimensional ratio w/1, is the ZT-cut crystal resonator described in French patent No. 2,435,855. The ZT-cut described in this patent will hereinafter be referred to as the ZTY-cut. Such a resonator, whose basic shape is a rectangle, can also have a more complex structure through the combination of several base rectangles which, from the point of view of the propagation of elastic waves, can be considered to be pseudo-free rectangles. Examples of such combinations can be found in the aforesaid patent, as well as in French patent No. 2,521,782, describing embeddable resonator structures with a so-called ZTY-cut.
ZTY-cut resonators are obtained from a Z cut quartz crystal (that is to say a quartz crystal having the optical axis Z perpendicular to the plane of the crystal), followed by a first rotation about the mechanical axis Y of the crystal, followed by a second rotation about an axis perpendicular to the plane of the resonator.
A ZTX-cut crystal resonator is described in French patent application No. 88 09221. Such a resonator is produced in a thin rectangular slice of crystal, whose width is directed along the electrical axis X of the crystal, whose length is directed along an axis Y' and whose thickness is directed along an axis Z', the axes Y' and Z' forming with the mechanical Y and optical Z axes of the crystal, respectively, an angle .phi. equal approximately to 24.degree. 24', and whose ratio w/1 of the width to the length is substantially equal to 0.64. When such a resonator is obtained by chemical etching of such a slice, it is easy to see that the lateral faces parallel to the axis Y' are in the favored plane of etching (the direction of the axis Z) and will, because of this, be exactly perpendicular to the large surfaces of the resonator.
The ZTX or ZTY-cut crystal resonators allow functioning in a range of frequencies below approximately 4 MHz. A resonator functioning in a higher range of frequencies can be obtained by a reduction of all the dimensions of the base structure of the resonator. Such a resonator would then require a slice thickness t of a value of approximately 30 .mu.m, a value very much lower than the value which can be used in practice, which is around 100 .mu.m.
The solution consisting of reducing the width w and the length l of the base structure of the resonator, while maintaining the thickness of the slice at an acceptable value, has the major disadvantage of increasing appreciably the impedance of the resonator.